Vehicle Bridge Interaction Modeling-Quarter Car-1D Bridge

This code provides a finite element modeling for the Vehicle Bridge Interaction Problem. The vehicle is modeled as a quarter car with two degrees of freedom accounting for the body mass bouncing and the axle mass bouncing. While the Bridge is modeled using Finite Element Euler Bernoulli Beams. The program can be used to simulate the VBI with and without road roughness. Also a damage model is added to simulate the effect of structural damages using Sinha Damage model (2002). The code is built upon the contact force concept. In this concept the vehicle equation of motion and the bridge equation of motion are solved separately by equating the contact force between the vehicle and the bridge. The equations of motion are solved explicitly using Newmark-Beta Integration scheme. For a very small time step size (dt<.001) implicit and explicit solution should match, thus the program is adequate to simulate the VBI for infinitesimal time steps. The code was written in Matlab-2018a, changes in language might be subjected in the future. There is a new technique that has been used to assemble the Bridge Stiffness matrix utilizing a positioning vector. The new approach enabled assembling the bridge stiffness matrix in only 10 lines. The computational time is relatively low: for 100 Finite beams, the solution time is 6sec using single core.